Abstract. In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, Derivation and double shuffle relations for multiple zeta values. Compos. Math. 142 (2)(2006), 307–338). After setting up the general framework we provide some numerical evidence for our two main conjectures. At the ...

To an arbitrary intersection of exceptional varieties of an embedded resolution we associate a nite number of congruences between naturally occurring multiplicities. This theory generalizes previous results concerning just one exceptional variety. Moreover we describe precise equalities which imply the congruences and we give some applications on the poles of Igusa's local zeta function.

biopolymers are environmental friendly sources as renewable and sustainable substituents for petroleum-based polymers. application of these polymers is common in variety of industries including papermaking. herbalexudate gums have been used in papermaking industry for decades, especially paper recycling. in this study, gum polysaccharide exudates from baridje plant  (ferula gummosa) extracted a...

This is the first report implementing combined density gradient centrifugation/Zeta (DGC/Zeta) sperm selection procedure for a couple with eleven previous intra cytoplasmic sperm injection/ in vitro fertilization (ICSI/IVF) failure cycles. Semen analysis was carried out according to World Health Organization criteria. Protamine deficiency, DNA fragmentation and morphology were assessed by chrom...

Let φ denote Euler’s phi function. For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n 6 x such that q ∤ φ(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for cyclotomic fields. In particular, we show that the Hardy-Littlewood conjecture about counts of prime k-tuples and a conjecture o...

We nd a condition for weights on the edges of a graph which insures that the Ihara zeta function has a 3-term determinant formula. Then we investigate the locations of poles of abelian graph coverings and compare the results with random covers. We discover that the zeta function of the random cover satis es an approximate Riemann hypothesis while that of the abelian cover does not.

Let φ denote Euler’s phi function. For a fixed odd prime q we give an asymptotic series expansion in the sense of Poincaré for the number Eq(x) of n ≤ x such that q ∤ φ(n). Thereby we improve on a recent theorem by B.K. Spearman and K.S. Williams [Ark. Mat. 44 (2006), 166–181]. Furthermore we resolve, under the Generalized Riemann Hypothesis, which of two approximations to Eq(x) is asymptotical...

A weak version of the Ihara formula is proved for zeta functions attached to quotients of the Bruhat-Tits building of PGL3. This formula expresses the zeta function in terms of Hecke-Operators. It is the first step towards an arithmetical interpretation of the combinatorially defined zeta function.

We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.

In this paper, partial Epstein zeta functions on binary linear codes, which are related with Hamming weight enumerators of binary linear codes, are newly defined. Then functional equations for those zeta functions on codes are presented. In particular, it is clarified that simple functional equations hold for partial Epstein zeta functions on binary linear self-dual codes.